Erratum: Ultrafine Entanglement Witnessing [Phys. Rev. Lett. 
<b>118</b>
, 110502 (2017)]

Shähandeh, Farid; Ringbauer, Martin; Loredo, J. C.; Ralph, Timothy C.

doi:10.1103/physrevlett.119.269901

Cited by 10 publications

(38 citation statements)

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“…Discussion of the results of Ref. [3] In this section we list the three main statements in Ref. [3] and give a detailed discussion of them.…”

Section: Criteria For Higher Dimensionsmentioning

confidence: 98%

“…[3] In this section we list the three main statements in Ref. [3] and give a detailed discussion of them. Two of the statements have already been corrected in the erratum [4], but it sometimes remains unclear, where precisely the mistake was made.…”

Section: Criteria For Higher Dimensionsmentioning

confidence: 99%

“…First, let us start with Theorem 1 of Ref. [3] for which it has already been pointed out that it requires a revision [4]. The original version of Theorem 1 in Ref.…”

Section: Criteria For Higher Dimensionsmentioning

confidence: 99%

“…The error in the proof in Ref. [3] is the following: The range of 0 is spanned by the vectors |00 and |11 and there are no other product vectors in the range. These product vectors do not lie in the plane characterized by Tr( C) = c. So, 0 constitutes already a counterexample to Lemma 3 in the Supplemental Material.…”

Section: Criteria For Higher Dimensionsmentioning

confidence: 99%

“…In this case, l = L (or c = C ) alone is clearly not sufficient to detect entanglement, so the question arises what conditions C and L have to fulfill in order to detect entanglement together. So far, a conjecture has been presented [3], but its rigorous derivation remained elusive.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

The structure of ultrafine entanglement witnesses

Gachechiladze¹,

Wyderka²,

Gühne³

2018

J. Phys. A: Math. Theor.

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An entanglement witness is an observable with the property that a negative expectation value signals the presence of entanglement. The question arises how a witness can be improved if the expectation value of a second observable is known, and methods for doing this have recently been discussed as so-called ultrafine entanglement witnesses. We present several results on the characterization of entanglement given the expectation values of two observables. First, we explain that this problem can naturally be tackled with the method of the Legendre transformation, leading even to a quantification of entanglement. Second, we present necessary and sufficient conditions that two product observables are able to detect entanglement. Finally, we explain some fallacies in the original construction of ultrafine entanglement witnesses [F. Shahandeh et al., Phys. Rev. Lett. 118, 110502 (2017)]. § Note that the numbering of the Lemmata in the Supplemental Material of Ref.[3] differs from the arxiv version.

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“…Discussion of the results of Ref. [3] In this section we list the three main statements in Ref. [3] and give a detailed discussion of them.…”

Section: Criteria For Higher Dimensionsmentioning

confidence: 98%

Section: Criteria For Higher Dimensionsmentioning

confidence: 99%

“…First, let us start with Theorem 1 of Ref. [3] for which it has already been pointed out that it requires a revision [4]. The original version of Theorem 1 in Ref.…”

Section: Criteria For Higher Dimensionsmentioning

confidence: 99%

Section: Criteria For Higher Dimensionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

The structure of ultrafine entanglement witnesses

Gachechiladze¹,

Wyderka²,

Gühne³

2018

J. Phys. A: Math. Theor.

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The Resource Theory of Entanglement

Shähandeh

2019

Springer Theses

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Quantitative coherence witness for finite dimensional states

Ren

Lin

et al. 2017

Annals of Physics

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We define the stringent coherence witness as an observable which has zero mean value for all of incoherent states and hence a nonzero mean value indicates the coherence. The existence of such witnesses are proved for any finite-dimension states. Not only is the witness efficient in testing whether the state is coherent, the mean value is also quantitatively related to the amount of coherence contained in the state. For an unknown state, the modulus of the mean value of a normalized witness provides a tight lower bound of l1-norm of coherence in the state. When we have some previous knowledge of the state, the optimal witness is derived such that its measured mean value, called the witnessed coherence, equals to the l1-norm of coherence. One can also fix the witness and implement some incoherent operations on the state before the witness is measured. In this case, the measured mean value cannot reach the witnessed coherence if the initial state and the fixed witness does not match well. Based this result, we design a quantum coherence game. Our results provides a way to directly measure the coherence in arbitrary finite dimension states and an operational interpretation of the l1-norm of coherence.

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Erratum: Ultrafine Entanglement Witnessing [Phys. Rev. Lett. 118 , 110502 (2017)]

Abstract: This corrects the article DOI: 10.1103/PhysRevLett.118.110502.

Cited by 10 publications

References 0 publications

The structure of ultrafine entanglement witnesses

The structure of ultrafine entanglement witnesses

The Resource Theory of Entanglement

Quantitative coherence witness for finite dimensional states

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